Many countries are trying to increase the recruitment to Science, Technology, Engineering and Mathematics (STEM) studies. Some have implemented curriculum reforms to this end, others may do so. Using experiences from curriculum reforms in Germany, the Netherlands and, in particular, Sweden, we consider a proposal from the Royal Society in England about a broader curriculum for 16-19-year-olds, involving more mathematics and science. In Sweden, a curriculum reform in 1995, for 16-20-year-olds, increased the academic content of vocational programmes, including mathematics and science, such that they provided eligibility to university studies. Another reform, in 2011, reinstated the distinctions between vocational and academic programmes and made courses yielding university eligibility compulsory for academic programmes only. Using longitudinal student population data for 1986-2017, we assess the reform outcomes through before-after comparisons. The 1995 reform was followed by "decreased" recruitment to STEM studies while the opposite was true for the 2011 reform. A reform in Germany requiring students to study more mathematics was not very successful, either. We connect the positive consequences following the 2011 reform to the extensive Swedish opportunities to change study path. Including the option to attend a 1-year 'add-on' education programme, enabling students with non-STEM upper secondary background to conduct STEM university studies, changes to STEM programmes dominate changes away from them. Accordingly, we recommend more, not less, flexibility in programme choice, preferably coupled with efforts to improve female STEM attitudes, which have proved effective in Sweden.